Abstract
Tolerance-based feature transforms (TFTs) assign to each pixel in an image not only the nearest feature pixels on the boundary (origins), but all origins from the minimum distance up to a user-defined tolerance. In this paper, we compare four simple-to-implement methods for computing TFTs on binary images. Of these methods, the Fast Marching TFT and Euclidean TFT are new. The other two extend existing distance transform algorithms. We quantitatively and qualitatively compare all algorithms on speed and accuracy of both distance and origin results. Our analysis is aimed at helping practitioners in the field to choose the right method for given accuracy and performance constraints.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Costa, L., Cesar Jr., R.: Shape analysis and classification. CRC Press, Boca Raton, USA (2001)
Cuisenaire, O.: Distance transformations: fast algorithms and applications to medical image processing. PhD thesis, Université catholique de Louvain, Belgium (1999)
Danielsson, P.-E.: Euclidean distance mapping. Computer Graphics and Image Processing 14(3), 227–248 (1980)
Foskey, M., Lin, M., Manocha, D.: Efficient computation of a simplified medial axis. In: Proc. of the 8th ACM symposium on Solid modeling and applications, pp. 96–107. ACM Press, New York (2003)
Lotufo, T., Falcao, A., Zampirolli, F.: Fast euclidean distance transform using a graph-search algorithm. In: Proc. of the 13th Brazilian Symp. on Comp., pp. 269–275 (2000)
Meijster, A., Roerdink, J., Hesselink, W.: A general algorithm for computing distance transforms in linear time. In: Goutsias, J., Vincent, L., Bloomberg, D. (eds.) Mathematical Morphology and its Applications to Image and Signal Processing, pp. 331–340. Kluwer Academic Publishers, Dordrecht (2000)
Mullikin, J.: The vector distance transform in two and three dimensions. CVGIP: Graphical Models and Image Processing 54(6), 526–535 (1992)
Musser, D., Saini, S.: STL tutorial and reference guide: C++ programming with the standard template library. Addison-Wesley Professional Computing Series. Addison-Wesley, Reading (1996)
Ogniewicz, R., Kübler, O.: Hierarchic voronoi skeletons. Pattern Recognition 28(3), 343–359 (1995)
Ragnemalm, I.: Neighborhoods for distance transformations using ordered propagation. CVGIP: Image Understanding 56(3), 399–409 (1992)
Sethian, J.: Level set methods and fast marching methods, 2nd edn. Cambridge University Press, Cambridge (1999)
Strzodka, R., Telea, A.: Generalized distance transforms and skeletons in graphics hardware. In: VisSym 2004. Proc. of EG/IEEE TCVG Symposium on Visualization, pp. 221–230. IEEE Computer Society Press, Los Alamitos (2004)
Telea, A., van Wijk, J.: An augmented fast marching method for computing skeletons and centerlines. In: Proc. of the symposium on Data Visualisation, pp. 251–259 (2002)
Telea, A., Vilanova, A.: A robust level-set algorithm for centerline extraction. In: Proc. of the symposium on Data Visualisation, pp. 185–194 (2003)
Verwer, B., Verbeek, P., Dekker, S.: An efficient uniform cost algorithm applied to distance transforms. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(4), 425–429 (1989)
Ye, Q.: The signed euclidean distance transform and its applications. In: Proc. of the 9th International Conference on Pattern Recognition, vol. 1, pp. 495–499 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Reniers, D., Telea, A. (2007). Tolerance-Based Feature Transforms. In: Braz, J., Ranchordas, A., Araújo, H., Jorge, J. (eds) Advances in Computer Graphics and Computer Vision. Communications in Computer and Information Science, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75274-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-75274-5_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75272-1
Online ISBN: 978-3-540-75274-5
eBook Packages: Computer ScienceComputer Science (R0)